How to show only a portion of an object based on its relation to another object?
if you mean, it should look like this: https://youtu.be/tpeUWpk1okM
then you can achieve this by
1.) adding a track to constraint from sphere to your object (red point)
2.) adding a box with a boolean modifier (intersect)
3.) adding a track to constraint from box to your object
4.) adding a copy location constraint to the box from object
5.) adding a limit distance constraint to sphere
a video tutorial is here: https://youtu.be/pww3BxVsko0
(please be a little bit patient, my internet upload speed is blazingly ...slow... :(
and this is why i love BLENDER - you add just some constraints, combine them and you got a perfect effect which is looking really amazing, without knowing anything about matrix, vertices, scalar product or python or mathematics ;)
UPDATE:
and here is a video where the realization of changing the subdivision surface depending on the location of another object is shown:
https://youtu.be/28SGevbNZKQ